Answered

Discover a wealth of knowledge at Westonci.ca, where experts provide answers to your most pressing questions. Connect with professionals on our platform to receive accurate answers to your questions quickly and efficiently. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

What is the amplitude of the function?

[tex]\[ y = 2 \cos \frac{\pi}{4} \left( x - \frac{1}{2} \right) \][/tex]

[tex]\[ \square \][/tex] (Type an integer or a simplified fraction.)

Sagot :

GinnyAnswer
To determine the amplitude of the given function, we analyze the general form of a cosine function, which is:

[tex]\[ y = A \cos(Bx - C) + D \][/tex]

Where:
- [tex]\( A \)[/tex] represents the amplitude of the function.
- [tex]\( B \)[/tex] affects the period of the function.
- [tex]\( C \)[/tex] represents the phase shift.
- [tex]\( D \)[/tex] represents the vertical shift.

The amplitude of the cosine function is the absolute value of the coefficient in front of the cosine term, [tex]\( A \)[/tex].

For the given function:

[tex]\[ y = 2 \cos \frac{\pi}{4} \left(x - \frac{1}{2}\right) \][/tex]

We can identify the coefficient [tex]\( A \)[/tex] as 2. Therefore, the amplitude is the absolute value of this coefficient.

Thus, the amplitude of the function is:

[tex]\[ \boxed{2} \][/tex]
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.